def test_projection_iga_fem(self):
from sfepy.discrete import FieldVariable
from sfepy.discrete.fem import FEDomain, Field
from sfepy.discrete.iga.domain import IGDomain
from sfepy.mesh.mesh_generators import gen_block_mesh
from sfepy.discrete.iga.domain_generators import gen_patch_block_domain
from sfepy.discrete.projections import (make_l2_projection,
make_l2_projection_data)
shape = [10, 12, 12]
dims = [5, 6, 6]
centre = [0, 0, 0]
degrees = [2, 2, 2]
nurbs, bmesh, regions = gen_patch_block_domain(dims, shape, centre,
degrees,
cp_mode='greville',
name='iga')
ig_domain = IGDomain('iga', nurbs, bmesh, regions=regions)
ig_omega = ig_domain.create_region('Omega', 'all')
ig_field = Field.from_args('iga', nm.float64, 1, ig_omega,
approx_order='iga', poly_space_base='iga')
ig_u = FieldVariable('ig_u', 'parameter', ig_field,
primary_var_name='(set-to-None)')
mesh = gen_block_mesh(dims, shape, centre, name='fem')
fe_domain = FEDomain('fem', mesh)
fe_omega = fe_domain.create_region('Omega', 'all')
fe_field = Field.from_args('fem', nm.float64, 1, fe_omega,
approx_order=2)
fe_u = FieldVariable('fe_u', 'parameter', fe_field,
primary_var_name='(set-to-None)')
def _eval_data(ts, coors, mode, **kwargs):
return nm.prod(coors**2, axis=1)[:, None, None]
make_l2_projection_data(ig_u, _eval_data)
make_l2_projection(fe_u, ig_u) # This calls ig_u.evaluate_at().
coors = 0.5 * nm.random.rand(20, 3) * dims
ig_vals = ig_u.evaluate_at(coors)
fe_vals = fe_u.evaluate_at(coors)
ok = nm.allclose(ig_vals, fe_vals, rtol=0.0, atol=1e-12)
if not ok:
self.report('iga-fem projection failed!')
self.report('coors:')
self.report(coors)
self.report('iga fem diff:')
self.report(nm.c_[ig_vals, fe_vals, nm.abs(ig_vals - fe_vals)])
return ok
def test_projection_iga_fem(self):
from sfepy.discrete import FieldVariable
from sfepy.discrete.fem import FEDomain, Field
from sfepy.discrete.iga.domain import IGDomain
from sfepy.mesh.mesh_generators import gen_block_mesh
from sfepy.discrete.iga.domain_generators import gen_patch_block_domain
from sfepy.discrete.projections import (make_l2_projection,
make_l2_projection_data)
shape = [10, 12, 12]
dims = [5, 6, 6]
centre = [0, 0, 0]
degrees = [2, 2, 2]
nurbs, bmesh, regions = gen_patch_block_domain(dims, shape, centre,
degrees,
cp_mode='greville',
name='iga')
ig_domain = IGDomain('iga', nurbs, bmesh, regions=regions)
ig_omega = ig_domain.create_region('Omega', 'all')
ig_field = Field.from_args('iga', nm.float64, 1, ig_omega,
approx_order='iga', poly_space_base='iga')
ig_u = FieldVariable('ig_u', 'parameter', ig_field,
primary_var_name='(set-to-None)')
mesh = gen_block_mesh(dims, shape, centre, name='fem')
fe_domain = FEDomain('fem', mesh)
fe_omega = fe_domain.create_region('Omega', 'all')
fe_field = Field.from_args('fem', nm.float64, 1, fe_omega,
approx_order=2)
fe_u = FieldVariable('fe_u', 'parameter', fe_field,
primary_var_name='(set-to-None)')
def _eval_data(ts, coors, mode, **kwargs):
return nm.prod(coors**2, axis=1)[:, None, None]
make_l2_projection_data(ig_u, _eval_data)
make_l2_projection(fe_u, ig_u) # This calls ig_u.evaluate_at().
coors = 0.5 * nm.random.rand(20, 3) * dims
ig_vals = ig_u.evaluate_at(coors)
fe_vals = fe_u.evaluate_at(coors)
ok = nm.allclose(ig_vals, fe_vals, rtol=0.0, atol=1e-12)
if not ok:
self.report('iga-fem projection failed!')
self.report('coors:')
self.report(coors)
self.report('iga fem diff:')
self.report(nm.c_[ig_vals, fe_vals, nm.abs(ig_vals - fe_vals)])
return ok
def test_projection_tri_quad(self):
from sfepy.discrete.projections import make_l2_projection
source = FieldVariable('us', 'unknown', self.field)
coors = self.field.get_coor()
vals = nm.sin(2.0 * nm.pi * coors[:, 0] * coors[:, 1])
source.set_data(vals)
name = op.join(self.options.out_dir,
'test_projection_tri_quad_source.vtk')
source.save_as_mesh(name)
mesh = Mesh.from_file('meshes/2d/square_quad.mesh',
prefix_dir=sfepy.data_dir)
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('bilinear',
nm.float64,
'scalar',
omega,
approx_order=1)
target = FieldVariable('ut', 'unknown', field)
make_l2_projection(target, source)
name = op.join(self.options.out_dir,
'test_projection_tri_quad_target.vtk')
target.save_as_mesh(name)
bbox = self.field.domain.get_mesh_bounding_box()
x = nm.linspace(bbox[0, 0] + 0.001, bbox[1, 0] - 0.001, 20)
y = nm.linspace(bbox[0, 1] + 0.001, bbox[1, 1] - 0.001, 20)
xx, yy = nm.meshgrid(x, y)
test_coors = nm.c_[xx.ravel(), yy.ravel()].copy()
vec1 = source.evaluate_at(test_coors)
vec2 = target.evaluate_at(test_coors)
ok = (nm.abs(vec1 - vec2) < 0.01).all()
return ok
def test_projection_tri_quad(self):
from sfepy.discrete.projections import make_l2_projection
source = FieldVariable('us', 'unknown', self.field)
coors = self.field.get_coor()
vals = nm.sin(2.0 * nm.pi * coors[:,0] * coors[:,1])
source.set_data(vals)
name = op.join(self.options.out_dir,
'test_projection_tri_quad_source.vtk')
source.save_as_mesh(name)
mesh = Mesh.from_file('meshes/2d/square_quad.mesh',
prefix_dir=sfepy.data_dir)
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('bilinear', nm.float64, 'scalar', omega,
approx_order=1)
target = FieldVariable('ut', 'unknown', field)
make_l2_projection(target, source)
name = op.join(self.options.out_dir,
'test_projection_tri_quad_target.vtk')
target.save_as_mesh(name)
bbox = self.field.domain.get_mesh_bounding_box()
x = nm.linspace(bbox[0, 0] + 0.001, bbox[1, 0] - 0.001, 20)
y = nm.linspace(bbox[0, 1] + 0.001, bbox[1, 1] - 0.001, 20)
xx, yy = nm.meshgrid(x, y)
test_coors = nm.c_[xx.ravel(), yy.ravel()].copy()
vec1 = source.evaluate_at(test_coors)
vec2 = target.evaluate_at(test_coors)
ok = (nm.abs(vec1 - vec2) < 0.01).all()
return ok
def test_variables(self):
from sfepy.discrete import FieldVariable, Integral
ok = True
u = FieldVariable('u',
'parameter',
self.field,
primary_var_name='(set-to-None)')
u.set_constant(1.0)
vec = u() # Nodal values.
_ok = nm.allclose(vec, 1.0)
self.report('set constant:', _ok)
ok = _ok and ok
def fun(coors):
val = nm.empty_like(coors)
val[:, 0] = 2 * coors[:, 1] - coors[:, 0]
val[:, 1] = coors[:, 0] + 3 * coors[:, 1]
return val
u.set_from_function(fun)
coors = u.field.get_coor()
eu = u.evaluate_at(coors)
_ok = nm.allclose(eu, fun(coors), rtol=0.0, atol=1e-13)
self.report('set from function:', _ok)
ok = _ok and ok
integral = Integral('i', order=2)
gu_qp = u.evaluate(mode='grad', integral=integral)
# du_i/dx_j, i = column, j = row.
gu = nm.array([[-1., 1.], [2., 3.]])
_ok = nm.allclose(gu_qp, gu[None, None, ...], rtol=0.0, atol=1e-13)
self.report('set from function - gradient:', _ok)
ok = _ok and ok
u_qp = gu_qp[..., :, :1]
u.set_from_qp(u_qp, integral)
vu = u()
_ok = (nm.allclose(vu[::2], -1, rtol=0.0, atol=1e-13)
and nm.allclose(vu[1::2], 2, rtol=0.0, atol=1e-13))
self.report('set from qp:', _ok)
ok = _ok and ok
return ok
def test_variables(self):
from sfepy.discrete import FieldVariable, Integral
ok = True
u = FieldVariable('u', 'parameter', self.field,
primary_var_name='(set-to-None)')
u.set_constant(1.0)
vec = u() # Nodal values.
_ok = nm.allclose(vec, 1.0)
self.report('set constant:', _ok)
ok = _ok and ok
def fun(coors):
val = nm.empty_like(coors)
val[:, 0] = 2 * coors[:, 1] - coors[:, 0]
val[:, 1] = coors[:, 0] + 3 * coors[:, 1]
return val
u.set_from_function(fun)
coors = u.field.get_coor()
eu = u.evaluate_at(coors)
_ok = nm.allclose(eu, fun(coors), rtol=0.0, atol=1e-13)
self.report('set from function:', _ok)
ok = _ok and ok
integral = Integral('i', order=2)
gu_qp = u.evaluate(mode='grad', integral=integral)
# du_i/dx_j, i = column, j = row.
gu = nm.array([[-1., 1.],
[ 2., 3.]])
_ok = nm.allclose(gu_qp, gu[None, None, ...], rtol=0.0, atol=1e-13)
self.report('set from function - gradient:', _ok)
ok = _ok and ok
u_qp = gu_qp[..., :, :1]
u.set_from_qp(u_qp, integral)
vu = u()
_ok = (nm.allclose(vu[::2], -1, rtol=0.0, atol=1e-13) and
nm.allclose(vu[1::2], 2, rtol=0.0, atol=1e-13))
self.report('set from qp:', _ok)
ok = _ok and ok
return ok